Generalized strictly diagonally dominant matrices play a wide and important role in computational mathematics, mathematical physics, theory of dynamical systems, etc.But it is difficult to judge a matrix is or not gen...Generalized strictly diagonally dominant matrices play a wide and important role in computational mathematics, mathematical physics, theory of dynamical systems, etc.But it is difficult to judge a matrix is or not generalized strictly diagonally dominant matrix.In this paper, by using the properties of α-chain diagonally dominant matrix, we obtain new criteria for judging generalized strictly diagonally dominant matrix, which enlarge the identification range.展开更多
In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
Recently, the diverse properties of Rydberg atoms, which probably arise from its large electric dipole moment （EDM）, have been explored. In this paper, we report electric dipole moments along with Stark energies and...Recently, the diverse properties of Rydberg atoms, which probably arise from its large electric dipole moment （EDM）, have been explored. In this paper, we report electric dipole moments along with Stark energies and charge densities of lithium Rydberg states in the presence of electric fields, calculated by matrix diagonalization. Huge electric dipole moments are discovered. In order to check the validity of the EDMs, we also use these electric dipole moments to calculate the Stark energies by numerical integration. The results agree with those calculated by matrix diagonalization.展开更多
In the paper,a necessary and sufficeent condition for generalized diagonal domiance matrices is given.Further, the relations among all generalized positive definite matrices are shown, also,some flaws and mistakes in...In the paper,a necessary and sufficeent condition for generalized diagonal domiance matrices is given.Further, the relations among all generalized positive definite matrices are shown, also,some flaws and mistakes in the references are corrected.展开更多
基金Supported by the National Natural Science Foundation of China（71261010）
文摘Generalized strictly diagonally dominant matrices play a wide and important role in computational mathematics, mathematical physics, theory of dynamical systems, etc.But it is difficult to judge a matrix is or not generalized strictly diagonally dominant matrix.In this paper, by using the properties of α-chain diagonally dominant matrix, we obtain new criteria for judging generalized strictly diagonally dominant matrix, which enlarge the identification range.
文摘In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
基金supported by the National Basic Research Program of China(Grant No.2012CB921603)the National Natural Science Foundation of China(GrantNos.61378039,61078013,61178009,and 11274209)+3 种基金the Program for Changjiang Scholars and Innovative Research Team in University,China(Grant No.IRT13076)the Fund for Fostering Talents in Basic Science of the National Natural Science Foundation of China(Grant No.J1210036)the Natural Science Foundation of Shanxi Province,China(Grant No.2012011003-2)the Shanxi International Collaboration Program,China(Grant No.2010081046)
文摘Recently, the diverse properties of Rydberg atoms, which probably arise from its large electric dipole moment （EDM）, have been explored. In this paper, we report electric dipole moments along with Stark energies and charge densities of lithium Rydberg states in the presence of electric fields, calculated by matrix diagonalization. Huge electric dipole moments are discovered. In order to check the validity of the EDMs, we also use these electric dipole moments to calculate the Stark energies by numerical integration. The results agree with those calculated by matrix diagonalization.
文摘In the paper,a necessary and sufficeent condition for generalized diagonal domiance matrices is given.Further, the relations among all generalized positive definite matrices are shown, also,some flaws and mistakes in the references are corrected.
